Question

show that root 3 is an irrational number ​

Answer 1

Refer attachment

The photo 1 is pg 2

Photo 2 is pg 1

Answer 2

let us assume to the contrary that root 3is irrational  than we get co primes a and b where b not equal to 0 such that root 3 =a/b.        than by squaring both sides we get 3=a2/b2.   now by to we get 3b2=a2 which implies 3 divides a2 and 3 divides a        let us assume a=3c bythis we get b2=3c2.             which implies that 3divides b.   but a and b are co primes and should have one common factor this contradiction is due to our wrong assumption that root 3is rational.   now we conclude  that root 3is irrational